end behavior of functions
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End Behavior of Functions. Lesson 2.4. Definitions. End behavior: A description of what happens to the values f(x) of a function f as x ∞ and as x - ∞ - PowerPoint PPT PresentationTRANSCRIPT
Lesson 2.4
End behavior: A description of what happens to the values f(x) of a function f as x ∞ and as x -∞
Asymptote: a line that the graph of a function y = f(x) approaches as the variable x approaches a fixed value or increases or decreases without bound.
The behavior of a function as x ∞ or as x -∞ falls into 1 of 3 categories.
1. Values approach real number L
2. The values of f(x) increase or decrease without bound; that is f(x)
∞ or f(x) - ∞
3. The values of f(x) follow neither 1 or 2.
= ∞
= 0
For example, cosine and sine functions
DNE
DNE
Probability of rolling an 8 with two dice
As the limit approaches ∞, it is approaching its theoretical probability, (14%).
Leading term: x4
Even- both do the same; positive: up!
Leading term: 4x3
Odd- different directions; positive- right up, left down!
Leading term: -1x4
even: do the same thing; negative: down!
Leading term: -2x5
Odd- different directions, negative – right down, left up!
Pages 102 – 103
2-14 evens, 18